Molar Mass Formula

Relates a sample's mass to the number of moles it contains using the substance's molar mass.

M = \frac{m}{n}

M = m/n

What it means

Molar mass is the bridge between the laboratory and the atomic scale. You cannot count atoms or molecules directly, but you can weigh them, and molar mass — the number of grams in one mole of a substance — converts between the mass on your balance and the mole count that balanced equations actually describe. A large molar mass means each mole weighs a lot (few, heavy particles), while a small molar mass means each gram contains many moles. When to use it: whenever you convert grams to moles or moles to grams before, during, or after a stoichiometry problem — it is almost always the first calculation in a mole-based solution.

Variables

Symbol	Name	Unit	Meaning
$M$	Molar mass	g/mol	The mass of one mole of the substance.
$m$	Mass	g	The mass of the sample, usually measured on a balance.
$n$	Amount of substance	mol	The amount of substance, the counting unit that balanced equations use.

Assumptions

The sample is a single pure substance, so its composition is uniform throughout.
Molar mass is calculated from standard atomic weights, which may differ slightly for samples with unusual isotopic composition.

Derivation

Molar mass is defined as the mass of one mole of a substance, M = m / n. Solving for mass gives m = n × M, and solving for moles gives n = m / M. It follows from the definition of the mole: since one mole of any substance has a known particle count, the mass-per-mole value converts directly between the macroscopic quantity we weigh and the mole count used in chemical equations.

Worked example

Problem

What mass of sodium chloride contains 2.50 mol of NaCl?

Given:

Mass of NaCl sample unknown; need grams from moles
n = 2.50 mol NaCl
Molar mass of NaCl = 22.990 + 35.45 = 58.4 g/mol

First find the molar mass: M(NaCl) = 22.990 + 35.45 = 58.440 g/mol, which rounds to 58.4 g/mol.
Rearrange the formula to solve for mass: m = n × M.
Substitute: m = 2.50 mol × 58.4 g/mol.
Multiply: 2.50 × 58.4 = 146 (the mol units cancel).

146 g NaCl

Weighing out 146 g of sodium chloride gives 2.50 mol of NaCl formula units, the amount needed to combine with the correct stoichiometric ratios in a balanced equation.